thermal paste works by filling the gaps between the metal on the top of your cpu and the metal on the bottom of the cooler with something other than air

usually the paste is made of something that conducts and transfers better than air does

from what I understand it is best to have just enough paste to fill whatever gaps will exist between the cpu and the heatsink (in theory it would almost be better to have metal on metal contact and everywhere the metal wasn't touching the gap was filled with paste)

to remove thermal paste rubbing alcohol and coffee filters are desired as the alcohol is non corrosive and great for cleaning while the coffee filters will not leave any dust behind

to apply thermal paste put a very small (smaller than a pea) sized amount on the center of the cpu
you can then use a plastic card to spread it out or you can just put the heatsink right on top of it (as you tighten the heatsink the paste will all even out anyway

the end

(on a side note: that picture reminds me of the tuniq tower)